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The sum of of the mean and variance of a binomial distribution is 15 and the sum of their squares is 117. the mean of the distribution is

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The sum of of the mean and variance of a binomial distribution is 15 and the sum of their squares is 117. the mean of the distribution is A. 6 B. 9 C. 3 D. 12 Select the correct answer from above options

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Correct Answer - B Let n and p be parameters of the binomial distribution . Then, np+npq=15and(np)2+(np)2+(npq)2=117 [Given] ∴ n2p2(1+q2) (np+npq)2 = 117 152 ⇒ 1+q2 (1+q)2 = 117 225 ⇒6q2-13q+6=0⇒q= 2 3 andp= 1 3 ∴np+npq=15⇒n× 1 3 +n× 2 9 =15⇒n=27

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